Another way to ask whether God can lie is this. The definition of deity is a Being who has all power (known as omnipotent) and who can do whatever he wills whenever he wants. If He has all these traits, which he does, then we could easily assume that he could "bear false witness" (Exodus 20:16). If he cannot do so, however, would this mean he was not a Deity worthy of worship?
There are two things, according to the Bible, that make it impossible for our heavenly Father to say something that is false. The book of Hebrews states something interesting regarding promises He has made to those who are Christians.
To those who were to receive what he promised, God wanted to make it very clear that he would never change his purpose . . . There are these two things, then, that cannot change and about which God cannot lie (Hebrews 6:17 - 18).
These two things involve the true hope that only Christians possess. The writer of Hebrews takes the next two chapters to explain in detail these two immutable (unchangeable) things.
Notice that Hebrews 7 deals with the greatness of the Melchizedek priesthood as opposed to the Aaronic priesthood. The hope for Israel was to be a great physical nation that would lead all nations to keep the commandments so they would have great physical blessings.
The oath of God, however, was to bring in a better hope, the awesome hope of eternal life as a member of his family inheriting the earth. This is one of the immutable things that will be accomplished in spiritual Israel (Hebrews 8:10).
What is the second immutable thing, however, that causes God not to lie? The book of Hebrews states, "The Lord swore and will not revoke His word, 'You are a Priest forever according to the order of Melchizedek' . . . but by the word of the swearing of the oath, which supersedes the law, the Son, Who has been perfected forever, has been made High Priest" (Hebrews 7:21, 28, HBFV).
God has decided that he will not lie because he has sworn to do two things. He first has sworn to make us (humans) into his very kind of people, which means to make us fully into his own image and likeness (Genesis 1:26). The second thing God promises is that Jesus will accomplish his ultimate purpose for us through the office of High Priest.
One of the seven things that the Eternal hates is someone who states something that is untrue (Proverbs 6:17). In fact, he will ultimately destroy those who habitually practice such behavior (Psalm 5:6). God does not lie because to do so would be to go against his holy, righteous character.